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A study of equilibrium states of a thermodynamic system whose evolution is governed not only by the temperature, but also by the ordering field is carried out. It is found that an adiabatically insulated system may have a new type of nonuniform state of equilibrium which is inhomogeneousin temperature.T he comparison is made of the stability conditions in isothermal and adiabatic systems. The steady motion of an interface boundary during a firstorder phase transition is investigated. It is shown, that depending upon the values of the diffusion coefficients, different regimes can exist. For small thermal diffusivity, the temperature of the final phase after the exothermal transition can be above the equilibrium point. The kinetic problem is reformulated to a dynamical system, and a numerical procedure to solve the latter is presented.N umerical results are discussedi n comparison with analytic ones